Question

Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 x 10^24 kg and of the Sun = 2 x 10^30 kg. The average distance between the two is 1.5 x 10^11 m.​

Answer 1

Given:-

→ Mass of earth = 6×10²⁴ kg

→ Mass of sun = 2×10³⁰ kg

→ Average distance between Earth and

Sun = 1.5×10¹¹ m

To find:-

→ Force of gravitation bewteen the Earth

and Sun.

Solution:-

By Universal Law of Gravitation, we know that :-

F = GMm/r²

Where :-

• F is the gravitational force between

the bodies.

• G is Universal Gravitational Constant.

• M is mass of the 1st body.

• m is mass of the 2nd body.

• r is the distance between the bodies.

_______________________________

• Value of G = 6.67×10⁻¹¹ Nm²/kg²

Substituting values, we get :-

=> F = 6.67×10⁻¹¹×6×10²⁴×2×10³⁰/(1.5×10¹¹)²

=> F = 6.67×10⁻¹¹×6×10²⁴×2×10³⁰/2.25×10²²

=> F = 6.67×6×2/2.25 × 10⁻¹¹⁺²⁴⁺³⁰⁻²²

=> F = 35.57×10²¹

=> F = 3.557×10²² N

Thus, force of gravitation between Earth and Sun is 3.557×10²²N .

Answer 2

We have,

Mass of Earth (let, m) = 6 × 10²⁴ kg

Mass of Sol (let, M) = 2 × 10³⁰ kg

Distance between them (d) = 1.5 × 10¹¹ m

We know,

F = GMm/d²

⇒F = [(6.7 × 10-¹¹ Nm²/kg²)(6 × 10²⁴ kg)(2 × 10³⁰ kg)]/[(1.5 × 10¹¹ m)²]

⇒F = (6.7 × 6 × 2)/(1.5)² × 10-¹¹+²⁴+³⁰-²²

⇒F = (6.7 × 12)/(1.5)² × 10²¹

⇒F = (80.4)/(2.25) × 10²¹

⇒F = 35.733 × 10²¹

[∵ 1 < k < 10,]

⇒F = 3.5733 × 10²² {Answer}